1. INTRODUCTION

Entrants have been identified as one important determinant of the market dynamic, especially the profitability of incumbents (McCann & Vroom, 2010; Kumar & Sudharshan, 1988; Simon, 2005). Incumbents can be affected, for instance, when entrants attempt to penetrate a market by reducing prices, which intensifies competition among firms (Besanko, Dranove, Shanley, & Schaefer, 2009; McCann & Vroom, 2010; Rumelt & Teece, 1994; Simon, 2005). In response, to avoid a confrontation that could lead to a destructive price war, incumbent firms often reposition their products or brands (Carpenter, 1989; Ellickson, Misra, & Nair, 2012; Hauser & Shugan, 2008; Trout & Ries, 1982). One well-known example of repositioning is Johnson & Johnson's Tylenol brand of analgesics. Tylenol once dominated the over-the-counter market for pain relief by esta- blishing the drug as effective with few side effects. After a competitor, Advil, entered the market in 1984, Tylenol revised its marketing to emphasize Tylenol's gentleness (Hauser & Shugan, 2008). Another example is U.S. local retailers' decision to shift their pricing formats after Walmart entered the market in the 1990s (Ellickson et al., 2012).

While repositioning can be advantageous, it may come at a cost because past strategic decisions, which often entail prior commitments (Ghemawat, 1991), may need to be changed. Typical costs associated with repositioning (“repositioning costs”) include investments to overcome within-firm managerial resistance to change, to rework channel relationships, and to educate (or advertise to) consumers about the new positioning (Menon & Dennis, 2017). These repositioning costs have substantial implications for the competitive interplay between firms (Ellickson et al., 2012; Wang & Shaver, 2014, 2016). Consider the case of Mobileye (Yoffie, 2014), a technology leader in vision technologies for advanced driver assistance systems (ADAS), which was highlighted in Menon and Yao (2017, p. 1954):

Rather than selling its technologies directly to original equipment manufacturers (OEMs), Mobileye initially partnered with Tier 1 automotive suppliers such as TRW and Autoliv who, in turn, sold the OEMs integrated ADAS using Mobileye and non-Mobileye vision technologies. Mobileye subsequently instituted an exclusivity policy under which it would  only work with Tier 1 suppliers who were not developing (or were no longer developing) non-Mobileye ADAS. While this policy change resulted in the loss of some partners (e.g., Autoliv), it led the remaining partners (e.g., TRW) to emphasize the development of complementary parts (i.e., non-camera technology) for a Mobileye-centered ADAS system while deemphasizing development of substitutes for Mobileye's vision technology. The success of automotive vision technologies depends on the technology's ability to accurately identify objects under varied driving conditions and accurate identification requires an object identification database that improves with extensive in-field use of the technology. Over time, then, the cost to a Mobileye current partner of repositioning itself to be a direct competitor of Mobileye is increasing, and, hence, Mobileye's policy change arguably benefits Mobileye by reducing the field of potential vision-technology competitors despite exploding ADAS demand.

Although repositioning costs play an important role in competitive interactions, entrants are often unable to precisely assess the incumbent's repositioning costs due to the prevalence of decision biases, systematic errors in how executives process information in strategic decision making (Horn, Lovallo, & Viguerie, 2005; Menon, 2018; Menon & Yao, 2018; Schwenk, 1984). These decision biases prevent managers from completely avoiding errors in estimating a competitor's ability (Goldfarb & Yang, 2009; Li, Petruzzi, & Zhang, 2016; Li, 2019; Prescott & Visscher, 1977). For example, using controlled laboratory studies, Moore and Cain (2007) and Cain, Moore, and Haran (2015) find that entrants to a market tend to systematically overestimate or underestimate their rivals. In a similar vein, using the data from U.S. local telephone markets shortly after the Telecommunications Act of 1996, Goldfarb and Xiao (2011) demonstrate that a new entrant's ability to predict the incumbent's behavior varies and depends on the manager experience and education of the new entrant. A similar bias exists for diversifying entrants as well as de novo ones. To illustrate, in the early 1990s, when Anheuser-Busch diversified to enter the snack food business, the beer giant greatly overestimated the repositioning costs of the incumbent, Frito-Lay, which repositioned itself efficiently (Horn et al., 2005; Stalk Jr. & Lachenauer, 2004).

Against this backdrop, this paper explores how firms' decision biases affect their performance outcomes, with entry/repositioning as the specific strategic context. While there is a rich tradition that recognizes the fundamental importance of decision biases in decision-making (Csaszar & Levinthal, 2016; Gavetti, 2012; Kaplan, 2011; Levinthal, 2011; Porac, Thomas, & Baden-Fuller, 1989; Zajac & Bazerman, 1991; Zhang, Gou, Liang, & Huang, 2013), this tradition has primarily taken a firm- centric perspective and paid relatively less attention to the impact of decision biases on competitive interactions. The strategic mental model approach is an attempt to address this gap by incorporating the role of cognition into game-theoretic analyses (Menon, 2018). Thus, we develop our strategic mental model within the incumbent repositioning context, focusing on three key components: parameter specification, parameter assessment, and belief system, as discussed below.

First, the specification of the key strategic parameter—incumbent repositioning costs—builds on the pioneering work of Ghemawat (1991) on a firm's commitment to making irreversible capacity decisions, but extends it to the positioning context with differentiated firms. In particular, the incumbent (she) is the market leader and initially a monopoly with the best possible market position. After the arrival of the entrant (he), the incumbent can adjust her position in order to differentiate herself from him. The repositioning costs of this adjustment depend on the incumbent's ability to change her activities, which we term “repositioning ability.” When a firm has a high repositioning ability, repositioning costs will be lower for a given degree of repositioning. This ability may, for instance, be related to a firm's possession of advanced machinery or technologies that facilitate the reconfiguration of its business processes (Eisenhardt & Martin, 2000; Helfat & Martin, 2015). The repositioning ability of an incumbent may be low for a variety of reasons such as existing commitments. Examples here include Apple's iPhone's commitment to using its own operating system and distribution channel (Ghemawat, 1991; Hill & Rothaermel, 2003; Pacheco-De-Almeida, Henderson, & Cool, 2008), a newspaper business's inability to reposition when Craigslist enters the local market (Seamans & Zhu, 2017), and Loblaw Companies Limited, a major grocery chain in Canada, that built superstores before Walmart entered the market, and that could not efficiently switch to a small-store format (Besanko et al., 2009).

Second, the strategic mental model emphasizes the need to study firms' ability to accurately assess the value of strategic parameters. This emphasis is important because the assumption of classical game-theoretical models that actors in the system have an accurate assessment of various relevant parameters is often violated by real-world firms (Kaplan, 2011; Levinthal, 2011; Menon, 2018; Simon, 1976). This means that, in our context, a new entrant, as the competitor of the incumbent, needs to assess the value of the incumbent's repositioning costs, and this assessment may be inaccurate. Thus, we use the term “underestimation bias” (“overestimation bias”) when the entrant underestimates (overestimates) the incumbent's repositioning ability.

Third, to incorporate decision bias into a game-theoretic analysis, one also needs to characterize firms' belief systems (Aumann & Brandenburger, 1995). In practice, incumbents may not know the entrant is biased and may also inaccurately assess the entrant's decisions. For example, as an incumbent motorcycle manufacturer, Harley Davidson inaccurately assessed Honda's entry into the U.S. lightweight motorcycle segment during the early 1960s (Menon, 2018; Pascale & Christiansen, 1989). In our context, an inaccurate assessment can mean that the incumbent is either unaware of entrant bias or has an awareness of entrant bias, but inaccurately perceives the level of bias. Although the entrant is biased on some level, the incumbent behaves as though the entrant were unbiased or differently biased.

The development of these three key components—repositioning costs, the entrant's assessment of repositioning costs, and the incumbent's belief system regarding the entrant—in turn sheds insights on each of these components. For repositioning costs, we illustrate their influence on the competitive interactions between incumbents and entrants by building on Ghemawat (1991) to develop a baseline model in which both firms are unbiased. If entrant position is exogenous, that is, the entrant position is not strategically determined by the entrant, the incumbent's profit always increases when she possesses a superior repositioning ability, because it allows her to efficiently differentiate herself from the entrant. When the entrant position is endogenous, that is, the entrant can strategically decide his position, the incumbent's superior repositioning ability also reduces the need for the entrant to differentiate, thus increasing competitive pressure on the incumbent and potentially reducing incumbent profit. These different outcomes result in two implications. First, the entrant's equilibrium profit can increase rather than decrease in relation to the incumbent's repositioning ability. Second, the incumbent faces less competition when her repositioning ability is lower. As a result, the incumbent's relative advantage, defined as the incumbent's relative performance over the entrant (Alcácer, Dezsö, & Zhao, 2015; Barney, 1991; Chatain & Zemsky, 2007; Pacheco-de Almeida & Zemsky, 2007), prevails, especially when the incumbent's repositioning ability is relatively low.

For the entrant's assessment on repositioning costs, we find that, consistent with intuition, both underestimation bias and overestimation bias lead to suboptimal positioning decisions, inevitably decreasing the entrant's performance. We find, however, that entrant bias can either increase or decrease the incumbent's performance, depending on the type of bias. In particular, the entrant's underestimation bias helps the incumbent, whereas his overestimation bias hurts the incumbent.

For the incumbent's belief system regarding the entrant, we first consider a setting where the incumbent does not accurately assess entrant bias despite having an awareness of it, that is, the incumbent anticipates a level of entrant bias that differs from his actual bias. In this setting, we find that, although incumbent bias always results in self-harm, it can boost the incumbent's performance relative to that of the entrant. To clarify, incumbent bias can be a drag on both the incumbent and the entrant; however, the drag for the entrant can be greater than the incumbent's losses due to her decision bias, enhancing her relative advantage. Perhaps more interestingly, in this setting where neither the incumbent nor the entrant has an accurate assessment of the other, both firms can actually earn more than in the baseline model where both firms are unbiased, depending on the values of repositioning costs and decision biases. This means that, although the incumbent's and entrant's respective biases always result in harm to the individual firm, firms can be better off when they both behave in a biased rather than an unbiased way. We further consider a setting in which the incumbent is completely unaware of the entrant's decision bias, rendering her even more biased. Interestingly, this increased bias does not necessarily inflict further self-harm on the incumbent. In fact, the incumbent's complete lack of awareness can simultaneously benefit both the incumbent and the entrant, leading to better performances for each firm compared with when the incumbent is aware of entrant bias (but has an inaccurate assessment), depending on the magnitude of the entrant's and incumbent's respective biases.

2. LITERATURE AND CONTRIBUTIONS

Although repositioning costs is a key aspect of strategy practice, the formal modeling of repositioning costs in strategy has only recently begun with Menon and Yao (2017). Their “starting point is Pankaj Ghemawat's (1991) theory of commitment as the essential element in identifying strategic choices. Ghemawat persuasively argues that a strategic choice is one that involves commitment and that committed choice creates the persistent pattern of action typically characterized as strategy” (Menon & Yao, 2017, p. 1954). Following this argument, Menon and Yao (2017) analytically investigate the interaction between an incumbent (innovator) and an entrant (follower). Within their setting, the incumbent develops and introduces a new product generation and then chooses to offer either generous or stingy licensing terms to a follower who can imitate the innovation or become a “complementor.” The follower's choices are modeled as involving possible repositioning costs because the activity systems supporting imitation versus complementarity are different. We add to this pioneering research by investigating the post-entry repositioning of the incumbent, one prevalent strategy in practice. We find that the entrant's equilibrium profit can increase rather than decrease in relation to the incumbent's repositioning ability, while the incumbent's relative advantage prevails if her repositioning ability is relatively low.

More importantly, we focus on settings where the entrant and the incumbent are not necessarily rational, thus contributing to the general realm of behavioral strategy (Cyert & March, 1963; Eggers & Kaplan, 2013; Gavetti, 2012; Helfat & Peteraf, 2015; Kaplan, 2011; Levinthal, 2011; Miller & Chen, 1994). While this literature is rich, it has paid little attention to the impact of decision biases on competitive interactions. Consequently, the literature calls for more research to incorporate decision biases into game-theoretic analyses (Menon, 2018). We follow this perspective to investigate the theoretical impact of decision biases in a strategic entry/repositioning context. When firms' biases are considered, this leads to counterintuitive results on firms' performance; although the prior behavioral strategy research often documents that decision biases harm firm performance, they can potentially be a positive force under certain conditions.

This paper also contributes to the literature on incumbent strategies in response to entrants enter- ing the market. These responses are among a firm's most important strategic decisions and have long been a central issue in economics, strategy, marketing, and operations (Dixit, 1979; Economides, 1984; Hauser & Shugan, 2008; McCann & Vroom, 2010; Modigliani, 1958). Recent studies have focused on one post-entry defense strategy available to incumbents—repositioning—and conclude that repositioning costs are fundamental to the strategic interactions of firms' activity systems (Ellickson et al., 2012). To model repositioning costs, we follow the tradition of Hotelling (1929) and numerous other works he inspired (e.g., Alcácer et al., 2015; Dixit & Stiglitz, 1977 and Thomas & Weigelt, 2000). In Hotelling's model without repositioning costs, each firm's equilibrium strategy is to locate at the ends of the market, maximally differentiating itself from its competitor (d'Aspremont, Gabszewicz, & Thisse, 1979). Most real-world examples, however, reveal a strategy that is more consistent with our theoretical prediction that firms are not necessarily located at the two ends of the Hotelling line. Accordingly, this paper offers insights that help reconcile the gap between theory and practice.

Also relevant to our work here is the literature on leader or follower relative performance, which forms the basis of the definition of relative advantage, a major area of research in strategic management (Barney, 1991; Hawk, Pacheco-De-Almeida, & Yeung, 2013; Lieberman & Montgomery, 1988, 1998). We enrich this literature by incorporating repositioning costs and decision biases into a classical model with differenti- ation and market entry. By doing so, we offer three observations. First, the incumbent can gain more profit than the entrant when her repositioning ability is relatively low rather than high. While the incumbent's repositioning ability benefits herself, it may also benefit the entrant by the same or an even greater amount. Second, although the entrant's estimation bias always hurts the entrant, this bias can enhance his advantage (as a follower) relative to the incumbent. Third, the incumbent's relative advantage is not necessarily lower than that of the entrant when she is biased rather than unbiased in perceiving the entrant's actions. The incumbent's lack of awareness as a decision bias can actually contribute to her own relative advantage.

3. CONCLUDING REMARKS

This paper develops a strategic mental model to examine the impacts of incumbent's repositioning costs and associated decision biases within a market entry setting. In our model setting, the entrant is biased on the first order belief, either overestimating or underestimating the incumbent's repositioning ability, whereas the incumbent can also be biased on the second order belief with regard to the entrant's bias, that is, the incumbent is biased in her assessment of entrant bias, despite having an awareness of it. We compare this setting to a baseline setting in which both the incumbent and the entrant are unbiased; the entrant perfectly assesses the incumbent's repositioning ability and the incumbent also knows the entrant's assessment. This comparison reveals that decision biases are not necessarily detrimental for firms, particularly when both the entrant and the incumbent are biased. In a similar vein, when the incumbent is more biased in the sense that she is completely unaware of entrant bias, we find that the incumbent's increasing bias can interestingly benefit both herself and the entrant.

Our core argument is that repositioning costs and the associated biases should be central factors to analyses of strategic dynamics in the context of market entry, which in turn has implications for several related literatures. First, this paper contributes to our understanding of how an incumbent responses to new firms entering the market, a central topic in the strategy literature (Ghemawat, 1991; King & Tucci, 2002; McCann & Vroom, 2010; Menon & Yao, 2017); we enrich this literature by incorporating decision biases of firms, following the lead of Menon (2018). Second, this paper contributes to the research on bias in estimating the skill of others (e.g., see Moore & Cain, 2007, Goldfarb & Xiao, 2011, and Cain et al., 2015). Although this literature often states that decision biases are detrimental, we find that a decision bias can be a positive force in the context of market entry and incumbent repositioning, which helps explain the prevalence of decision biases in market entry (Besanko et al., 2009). Third, our study also adds to a long-standing literature concerning differentiation (Alcácer et al., 2015; Dixit & Stiglitz, 1977; Hotelling, 1929; Thomas & Weigelt, 2000). This literature traditionally suggests that each firm's equilibrium strategy is to locate itself at one of two ends of the market, opposite its competitor (d'Aspremont et al., 1979). Our model predicts that firms can locate at any position along the Hotelling line, depending on the repositioning costs and decision biases. This helps reconcile the gap between the traditional theory and real-world examples which often reveal that firms are not necessarily located at the ends of the Hotelling line.

Our results also have implications for strategic interactions between multi-divisional firms competing across geographies or product markets. Suppose the incumbent (entrant) has a sister incumbent (brother entrant) owned by the same parent corporation. If the sister incumbent has experience with the entry of the brother entrant, then the incumbent's own repositioning costs can be affected as a result of learning from prior repositioning across sibling units (Alcácer et al., 2015; Alcácer & Zhao, 2012; Kalnins & Mayer, 2004; Seamans & Zhu, 2017). In such a context, our analysis indicates that changed repositioning costs can lead to a lower or higher performance for the incumbent, and a greater or smaller benefit for the entrant than for the incumbent. Hypothetically, the sister incumbent could also learn the importance of having “sticky” commitments, and thus instead increase her commitment to the current position. In light of our results, researchers and practitioners should look beyond the positive or negative effect of repositioning ability on the focal incumbent firm's absolute performance, which is the primary focus of the existing literature; what they should also consider is the possible negative effect on an incumbent's relative performance vis-á-vis competitive entrants, which is often an important strategic concern for firms.

This paper takes one of the first analytical steps toward examining the impacts of decision biases associated with repositioning costs. While we believe that our results can apply broadly to different types of post-entry repositioning across different contexts, we acknowledge the possibility that our key insights may change in other contexts, and exploring that can drive future research. For example, we focus on one key strategic parameter, repositioning cost, and consequently, the biases we model are around this parameter. Future research can examine the biases associated with other important strategic parameters, such as the promise of different technological trajectories (Wu, Wan, & Levinthal, 2014), or more broadly, the very existence of certain actors or actions related to mental models (Levinthal, 2011; Menon, 2018). Moreover, we study decision biases on the first order belief and the second order belief regarding repositioning cost. Future research could also examine higher order beliefs.

We also acknowledge that, as is the case with many other strategic mental models, our model can also lead to situations with inconsistency between the observed outcomes and the beliefs of the firms. In practice, firms may simply ignore such inconsistency or deny its validity (Menon, 2018). For such firms, the key insights in this paper can directly apply. However, for firms learning from the inconsis- tency to recalibrate their assessments of the biases, it is often challenging to identify how they should learn from observed outcomes to update their mental model (Menon & Yao, 2018). We are able to conduct a preliminary analysis of a two-period dynamic model, where we find that the managerial insights in Propositions 2 and 4 remain robust. Future research may further address this inconsistency issue by examining settings in which the incumbent and entrant interact for longer periods, or focus- ing on a subset of the problem and equilibria such as self-confirming equilibria (Ryall, 2003), or even exploring conditions in which a firm should resolve the inconsistency versus ignoring it.

On the empirical front, future work could follow approaches in the empirical literature (Galasso & Simcoe, 2011; Wang & Shaver, 2014, 2016) to classify different types of decision biases and different repositioning costs and then accordingly determine market entry decisions together with the associated firms' performance. For settings where firms are likely to be biased about each other (e.g., Shleifer, 2000), one may also empirically identify conditions in which decision biases can lead to lower or higher profits. Such an empirical effort would not only test the predictions of the current model, but also offer guidelines for the design and adoption of strategies aimed at enhancing repositioning ability and curtailing executives' biases.

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